Manuscript Hawk01-B@1 · Hawk01-B.tex · definition · cfa976f1

Definition: Recovery and leakage

Preservation criteria and the complete complement · lines 232–250

Hawk01-B@1#def:errors, Hawk01-B@1#eq:recovery, Hawk01-B@1#eq:leakage

The unrestricted deterministic recovery error and inaccessible leakage distance are

ϵ_{rec} (t) δ_{leak} (t) = D_{t} : Z_{t} \to A in f D_{⋄} (D_{t} N_{t}, id_{A}), = τ_{F_{t}} in f D_{⋄} (C_{t}, T_{τ_{F_{t}}}), T_{τ} (X) = Tr (X) τ .

The decoder optimization is over CPTP maps. A resource-restricted decoder class defines a different optimum.

Displayed formulas in this passage

Hawk01-B@1#eq:recovery · line 236
$ϵ_{rec} (t) δ_{leak} (t) = D_{t} : Z_{t} \to A in f D_{⋄} (D_{t} N_{t}, id_{A}), = τ_{F_{t}} in f D_{⋄} (C_{t}, T_{τ_{F_{t}}}), T_{τ} (X) = Tr (X) τ .$
Hawk01-B@1#eq:leakage · line 236
$ϵ_{rec} (t) δ_{leak} (t) = D_{t} : Z_{t} \to A in f D_{⋄} (D_{t} N_{t}, id_{A}), = τ_{F_{t}} in f D_{⋄} (C_{t}, T_{τ_{F_{t}}}), T_{τ} (X) = Tr (X) τ .$